OK, I have seen lots of people hold the lead rope in a loop.
see her left hand?
That can be a dangerous way to hold it. Imagine you were holding her horse and the lead rope was like that. Your horse suddenly got scared and turned away quickly and started walking or trotting away. What is the lead rope going to do? Well, because you might have been holding it in a loop, when the horse walks away - the loop will tighten around your fingers. If he's trotting or loping, it'll tighten around your fingers and bad things can happen.
So in my opinion - holding it like this is safer:
I call it the figure 8 style, because the way the rope is held, it looks like a figure eight. (this was the best photo I could find..)
This is safer, because when the horse would become scared and move away pretty fast, then instead of your fingers getting mushed together, then you have all this extra rope to try and get your horse to come back to you - and you can still do it because your hand isn't mashed up between the rope, or worse.
I tried to find a video, but there wasn't any.
This is just thought, no judging and no saying "holding the rope in a loop is wrong," because I am not trying to say that. Just concerning a little bit more safety. Better safe than sorry! Haha!